Q: A student’s grades and credit hours are as follows: A (3 credits), B (4 credits), C (3 credits). Using the point system A=4, B=3, C=2, what is the weighted mean (GPA)?

$$\frac{(4 \times 3) + (3 \times 4) + (2 \times 3)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

Q: A frequency distribution for a sample is given. The midpoints are 10, 20, 30, 40, and the corresponding frequencies are 2, 5, 7, 6. What is the estimated sample mean?

$$\frac{(10 \times 2) + (20 \times 5) + (30 \times 7) + (40 \times 6)}{2 + 5 + 7 + 6} = \frac{20 + 100 + 210 + 240}{20} = \frac{570}{20} = 28.5$$

Question 1

A frequency distribution is constructed for a data set of exam scores ranging from 42 to 98. If you want to use 8 classes, what is the appropriate class width to use?

Accepted Answer

$$\frac{98 - 42}{8} = 7$$; so use a class width of 8

Question 2

Given the following class limits for a frequency distribution: 10–19, 20–29, 30–39, what are the class boundaries for the first class?

Accepted Answer

$$9.5$$ and $$19.5$$

Question 3

A data set of 50 values is grouped into a frequency distribution with 5 classes. The frequencies for the classes are 5, 10, 15, 10, and 10. What is the relative frequency of the third class?

Accepted Answer

$$\frac{15}{50} = 0.30$$

Question 4

Which of the following statements about histograms and bar graphs is TRUE?

Accepted Answer

Bars in a histogram touch each other, while bars in a bar graph are separated by spaces.

Question 5

A cumulative frequency graph (ogive) is constructed by plotting cumulative frequencies at which points on the horizontal axis?

Accepted Answer

At the upper class boundaries

Question 6

A stem-and-leaf plot is constructed for the following data: 23, 27, 31, 35, 35, 38, 41. What is the correct stem-and-leaf representation for the 30s?

Accepted Answer

3 | 1 5 5 8

Question 7

Which of the following best describes a Pareto chart?

Accepted Answer

A vertical bar graph with bars in decreasing order of frequency

Question 8

A scatter plot is most useful for which of the following purposes?

Accepted Answer

Displaying the relationship between two quantitative variables

Question 9

Given the data set: 4, 7, 7, 9, 10, 12, 15, what is the median?

Accepted Answer

9

Question 10

A sample of 5 students has test scores: 80, 85, 90, 95, 100. What is the sample mean?

Accepted Answer

$$\frac{80 + 85 + 90 + 95 + 100}{5} = 90$$

Question 11

A data set has the following values: 2, 2, 3, 4, 5, 5, 5, 6. What is the mode?

Accepted Answer

5

Question 12

A student’s grades and credit hours are as follows: A (3 credits), B (4 credits), C (3 credits). Using the point system A=4, B=3, C=2, what is the weighted mean (GPA)?

Accepted Answer

$$\frac{(4 	imes 3) + (3 	imes 4) + (2 	imes 3)}{3 + 4 + 3} = \frac{12 + 12 + 6}{10} = 3.0$$

Question 13

A frequency distribution for a sample is given. The midpoints are 10, 20, 30, 40, and the corresponding frequencies are 2, 5, 7, 6. What is the estimated sample mean?

Accepted Answer

$$\frac{(10 	imes 2) + (20 	imes 5) + (30 	imes 7) + (40 	imes 6)}{2 + 5 + 7 + 6} = \frac{20 + 100 + 210 + 240}{20} = \frac{570}{20} = 28.5$$

Question 14

Which of the following distributions is most likely to have the mean less than the median?

Accepted Answer

A distribution that is skewed left

Question 15

A data set has a minimum value of 12 and a maximum value of 47. What is the range?

Accepted Answer

$$47 - 12 = 35$$

Question 16

Given a population data set: 2, 4, 6, 8, what is the population variance?

Accepted Answer

$$\$$sigma^2$$ = \frac{(2-5)^2$ + (4-5)^2$ + (6-5)^2$ + (8-5)^2$}{4} = \frac{9 + 1 + 1 + 9}{4} = \frac{20}{4} = 5$$

Question 17

A sample has a mean of 50 and a standard deviation of 5. According to the Empirical Rule, approximately what percent of the data falls between 45 and 55?

Accepted Answer

About 68%

Question 18

Chebychev’s Theorem states that for any data set, at least what percent of the data lies within 3 standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{3^2$} = 1 - \frac{1}{9} = \frac{8}{9} \approx 88.9\%$$

Question 19

The heights (in inches) of a basketball team have a mean of 75 and a standard deviation of 3. The weights (in pounds) have a mean of 200 and a standard deviation of 20. Which group has more relative variation?

Accepted Answer

Weights, because $$\frac{20}{200} = 0.10 is $$greater than $$\frac{3}{75} = 0.04$$

Descriptive Statistics: Frequency Distributions, Graphs, Measures of Central Tendency, and Variation

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